Question: Simplify; express your answer in exponential form. Assume $x\neq 0, p\neq 0$. $\dfrac{{x^{5}}}{{(x^{-2}p^{-5})^{-5}}}$
Answer: To start, try working on the numerator and the denominator independently. In the numerator, we have ${x^{5}}$ to the exponent ${1}$ . Now ${5 \times 1 = 5}$ , so ${x^{5} = x^{5}}$ In the denominator, we can use the distributive property of exponents. ${(x^{-2}p^{-5})^{-5} = (x^{-2})^{-5}(p^{-5})^{-5}}$ Simplify using the same method from the numerator and put the entire equation together. $\dfrac{{x^{5}}}{{(x^{-2}p^{-5})^{-5}}} = \dfrac{{x^{5}}}{{x^{10}p^{25}}}$ Break up the equation by variable and simplify. $\dfrac{{x^{5}}}{{x^{10}p^{25}}} = \dfrac{{x^{5}}}{{x^{10}}} \cdot \dfrac{{1}}{{p^{25}}} = x^{{5} - {10}} \cdot p^{- {25}} = x^{-5}p^{-25}$.